As a Maltese citizen, I think I can tell you, at the start of the cold war both superpowers were anti-imperialist and because they were stronger than European countries, countries like France, The U.K, Portugal, etc began a process of decolonization, whether it be fighting a war to keep colonies or peacefully transferring power.

This was the case with The U.K and Malta, Malta was important militarily as it is positioned in the middle of the Mediterranean, the Maltese wanted representation to have a say on military defense spending on Malta, in 1950 elections were held in Malta and a man by the name of Enrico Mizzi from the Maltese nationalist party (Partit Nazzjonalista) was elected, until he died 3 months later, he was replaced by Gorg Borg Olivier, the nationalist party was keen on the idea of independence from the U.K which soured the relationship with the British government, add to that he almost bankrupted Malta on vote winning policies, because he was running out of money he kept demanding the British government more money whilst simultaneously wanting more autonomy, in 1955 Malta had yet another election which saw Dom Mintoff of the Labour party (Partit Laburista) elected, the Labour party wanted to be integrated MORE with the U.K, Dom mintoff introduced an idea to the British government, to annex Malta, The U.K was content with this as they could keep their colony and the U.S couldn't say anything.

Talks began to see how to integrate Malta into the U.K and they came up with an idea, they agreed that Malta would become a constituent nation of the U.K and would hold a position similar to that of Northern Ireland, with it's own local representation and 3 members in the House of Commons, this would have been good to Malta, as Malta wasn't in a favourable position with it's economy, the Maltese were also aware of their strategic importance and would have given them a small voice in maintaining defense on the island, it would also have allowed Maltese citizens access to british social programs, in 1956 Malta held a referendum to join the U.K or not, yes won with 77% of the vote on 60% turnout.

There were several reasons for why Malta didn't join:

1)Membership of the U.K was conditional on Malta reining in it's spending and limiting the government to a small budget deficit, which Mintoff resigned in protest for.

2)Many in the British government were worried that Malta joining the U.K would set a precedent for other imperial colonies.

3)During the course of the 1950's British defense needs changed and Malta began losing it's strategic importance as a naval base.

For these reasons, the U.K saw that they were going to subsidize the island for very little, negotiations fell down and Malta gained it's independence in 1964.